| Popis: |
This thesis discusses recent advances in a variety of areas in multi-parametric programming and explicit model predictive control (MPC). First, novel theoretical and algorithmic results for multi-parametric quadratic and mixed-integer quadratic programming (mp-QP/mp- MIQP) problems extend the current state-of-the-art: for mp-QP problems, it is shown that its solution is given by a connected graph, based on which a novel solution procedure is developed. Furthermore, several computational studies investigate the performance of different mp-QP algorithms, and a new parallelization strategy is presented, together with an application of mp-QP algorithms to multi-objective optimization. For mp-MIQP problems, it is shown that it is possible to obtain the exact solution of a mp-MIQP problem without resorting to the use of envelopes of solutions, whose computational performance is compared in a computational study with different mp-MIQP algorithms. Then, the concept of robust counterparts in robust explicit MPC for discrete-time linear systems is revisited and an elegant reformulation enables the solution of closed-loop robust explicit MPC problems with a series of projection operations. This approach is extended to hybrid systems, where the same properties are proven to hold. Finally, a new approach towards unbounded and binary parameters in multi-parametric programming is introduced, and several examples highlight its potential. Open Access |
